The hyper-ideal vertex scale b is floored to keep the geometry valid. The
original clamp `b<0 → 0.01` mirrors the Java oracle but is only C⁰ (in fact
value-discontinuous at b=0): a Newton step crossing the feasibility boundary
hits a kink that can stall convergence (numerical-stability audit N3).
Rather than replace the Java-faithful behaviour (which would break the golden
parity tests), make the floor a selectable mode so BOTH the Java standpoint
and the clean mathematics are available:
- HyperIdealScaleClamp::HardJava (DEFAULT) — the original snap, bit-for-bit
faithful to HyperIdealFunctional.java → all parity tests unchanged.
- HyperIdealScaleClamp::SmoothBarrier — C¹ softplus floor
b ↦ floor + softplus_β(b−floor), β = HYPER_IDEAL_SCALE_SHARPNESS (=100);
≈ identity away from the floor, smooth across b=0. Opt-in.
clamp_hyper_ideal_scale centralises the logic (also folds in the N4 nachzügler:
compute_face_angles used a bare 0.01). The mode threads with a defaulted
trailing parameter through compute_face_angles, face_angles_from_local_dofs,
evaluate_hyper_ideal, the four hyper_ideal_hessian* variants and
newton_hyper_ideal — so every existing call site keeps HardJava behaviour.
Tests (+4): clamp-function C¹/floor/identity contract, mode-equivalence away
from the boundary, and end-to-end SmoothBarrier convergence to the same Java
golden vector (LawsonHyperIdeal). 296/296 CGAL tests pass.
Documented in doc/math/geometry-modes.md.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Second Lawson variant from HyperIdealConvergenceTest...WithBranchPoints.
- make_lawson_branch_points(): base + STELLAR subdivision (Java StellarLinear)
via CGAL Euler::add_center_vertex — a centre vertex per quad fan-connected to
its 4 corners (6 centres, 24 triangles, 36 edges). The 6 centres are IDEAL
vertices (b=0, v_idx=-1); θ_e=π on the 12 base edges, θ_e=π/2 on the 24 spokes.
- BranchPointsGoldenVector_JavaXVal: newton_hyper_ideal converges to the Java
golden (per symmetry class @1e-4):
original vertices → 1.3169579
base edges → 2.2924317
spoke edges → 0 (the π/2 spokes collapse to ideal)
Key insight: Java's index-based θ split (first 12 edges π, rest π/2) is
geometric — base edges vs stellar spokes — so the symmetry shortcut applies.
createLawsonHyperelliptic() NOT ported: needs a reader for the Java
conformal-data XML (lawson_curve_source.xml) + a port of
HyperIdealHyperellipticUtility, and its golden vector is not class-symmetric.
Documented as a deferred task.
243/243 cgal tests pass.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Ports the Java HyperIdealConvergenceTest (Lawson square-tiled) — the strongest
remaining @Ignore'd oracle (a hard-coded converged solution from a historical
x86 PETSc run).
- make_lawson_square_tiled(): builds the genus-2 base (4 vertices, 12 edges,
6 quads) via the low-level CGAL Surface_mesh half-edge API (add_edge +
set_target/set_next/set_face/set_halfedge), since the multi-edges (≥2 edges
per vertex pair) make add_face / OFF / polygon-soup impossible. Then
triangulate_faces → 12 triangles, 18 edges (12 original + 6 diagonals).
BuildsValidGenus2Mesh: is_valid + V=4/F=12/E=18 + χ=−2.
- ConvergenceGoldenVector_JavaXVal: Θ_v=2π, θ_e=π/2 (12 original edges),
θ_e=π (6 diagonals); newton_hyper_ideal converges (from x0=1.0, unconstrained)
to the Java golden vector:
vertices → 1.1462158341786262
original → 1.7627471737467797
aux → 2.633915794495759
asserted per symmetry class @1e-5 (robust to DOF ordering).
The perfect symmetry of the golden vector means any consistent one-diagonal
triangulation reproduces the three values, so the external jtem Triangulator
choice need not be replicated. Resolves the Tier-3 item from PR #29's analysis.
242/242 cgal tests pass.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
